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#include "tommath_private.h"
#ifdef BN_MP_LOG_U32_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
/* SPDX-License-Identifier: Unlicense */
/* Compute log_{base}(a) */
static mp_word s_pow(mp_word base, mp_word exponent)
{
mp_word result = 1u;
while (exponent != 0u) {
if ((exponent & 1u) == 1u) {
result *= base;
}
exponent >>= 1;
base *= base;
}
return result;
}
static mp_digit s_digit_ilogb(mp_digit base, mp_digit n)
{
mp_word bracket_low = 1u, bracket_mid, bracket_high, N;
mp_digit ret, high = 1u, low = 0uL, mid;
if (n < base) {
return 0uL;
}
if (n == base) {
return 1uL;
}
bracket_high = (mp_word) base ;
N = (mp_word) n;
while (bracket_high < N) {
low = high;
bracket_low = bracket_high;
high <<= 1;
bracket_high *= bracket_high;
}
while (((mp_digit)(high - low)) > 1u) {
mid = (low + high) >> 1;
bracket_mid = bracket_low * s_pow(base, (mp_word)(mid - low));
if (N < bracket_mid) {
high = mid ;
bracket_high = bracket_mid ;
}
if (N > bracket_mid) {
low = mid ;
bracket_low = bracket_mid ;
}
if (N == bracket_mid) {
return (mp_digit) mid;
}
}
if (bracket_high == N) {
ret = high;
} else {
ret = low;
}
return ret;
}
/* TODO: output could be "int" because the output of mp_radix_size is int, too,
as is the output of mp_bitcount.
With the same problem: max size is INT_MAX * MP_DIGIT not INT_MAX only!
*/
mp_err mp_log_u32(const mp_int *a, uint32_t base, uint32_t *c)
{
mp_err err;
mp_ord cmp;
uint32_t high, low, mid;
mp_int bracket_low, bracket_high, bracket_mid, t, bi_base;
err = MP_OKAY;
if (a->sign == MP_NEG) {
return MP_VAL;
}
if (MP_IS_ZERO(a)) {
return MP_VAL;
}
if (base < 2u) {
return MP_VAL;
}
/* A small shortcut for bases that are powers of two. */
if ((base & (base - 1u)) == 0u) {
int y, bit_count;
for (y=0; (y < 7) && ((base & 1u) == 0u); y++) {
base >>= 1;
}
bit_count = mp_count_bits(a) - 1;
*c = (uint32_t)(bit_count/y);
return MP_OKAY;
}
if (a->used == 1) {
*c = (uint32_t)s_digit_ilogb(base, a->dp[0]);
return err;
}
cmp = mp_cmp_d(a, base);
if ((cmp == MP_LT) || (cmp == MP_EQ)) {
*c = cmp == MP_EQ;
return err;
}
if ((err =
mp_init_multi(&bracket_low, &bracket_high,
&bracket_mid, &t, &bi_base, NULL)) != MP_OKAY) {
return err;
}
low = 0u;
mp_set(&bracket_low, 1uL);
high = 1u;
mp_set(&bracket_high, base);
/*
A kind of Giant-step/baby-step algorithm.
Idea shamelessly stolen from https://programmingpraxis.com/2010/05/07/integer-logarithms/2/
The effect is asymptotic, hence needs benchmarks to test if the Giant-step should be skipped
for small n.
*/
while (mp_cmp(&bracket_high, a) == MP_LT) {
low = high;
if ((err = mp_copy(&bracket_high, &bracket_low)) != MP_OKAY) {
goto LBL_ERR;
}
high <<= 1;
if ((err = mp_sqr(&bracket_high, &bracket_high)) != MP_OKAY) {
goto LBL_ERR;
}
}
mp_set(&bi_base, base);
while ((high - low) > 1u) {
mid = (high + low) >> 1;
if ((err = mp_expt_u32(&bi_base, (uint32_t)(mid - low), &t)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_mul(&bracket_low, &t, &bracket_mid)) != MP_OKAY) {
goto LBL_ERR;
}
cmp = mp_cmp(a, &bracket_mid);
if (cmp == MP_LT) {
high = mid;
mp_exch(&bracket_mid, &bracket_high);
}
if (cmp == MP_GT) {
low = mid;
mp_exch(&bracket_mid, &bracket_low);
}
if (cmp == MP_EQ) {
*c = mid;
goto LBL_END;
}
}
*c = (mp_cmp(&bracket_high, a) == MP_EQ) ? high : low;
LBL_END:
LBL_ERR:
mp_clear_multi(&bracket_low, &bracket_high, &bracket_mid,
&t, &bi_base, NULL);
return err;
}
#endif
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